Smooth particle hydrodynamics simulations of long-duration violent three-dimensional sloshing in tanks

Abstract

We present a smooth particle hydrodynamics (SPH) formulation that captures the sloshing frequencies of tanks and accurately simulates long-duration violent sloshing in partially filled tanks of arbitrary shape. The SPH simulations are performed using a modified version of the open-source code DualSPHysics that incorporates a density-based stabilization (δ-SPH) and imposes wall boundary conditions via ghost particles in order to achieve pressure fields without spurious spatial oscillations and to reduce non-physical energy dissipation. We verify the SPH scheme by showing that calculated sloshing wave heights, forces and natural sloshing frequencies of tanks of simple shapes, namely rectangular, cylindrical upright and spherical, match the analytical values given by the potential theory in the linear regime. The scheme is then validated by predicting the sloshing frequencies obtained experimentally in a toroidal tank and in a pill-shaped tank. Finally, we present a study of a pill-shaped tank subject to a long period of external forcing comparing simulated sloshing forces to experimental values obtained by ESA/ESTAC. The simulation is shown to fairly accurately reproduce the sloshing forces and predict the transition to swirling wave motion. Analysis of the frequency range further showed good agreement of the dominant frequencies between the experimental and simulated forces.